What is loan amount with payment of 326.50 for 36 months?

1 Answer

Answer :

WITHOUT KNOWING the interest rate, and whether the interest issimple or compounded, and how often the latter is applied, it isIMPOSSIBLE to answer the question.As the interest rate, the type of interest and how often it isapplied is NOT given, the answer cannot be given.All I can give you is a formula for you to work it outyourself:A loan will usually be charged at compound interest compoundedevery month.Let L = amount of LoanLet r = monthly rate (see below)Let p = payment per monthThe rate r is not quite the specified APR.The APR is given as a percentage: APR = apr% = apr/100Assume that no repayments are made. Then interest is added ontothe interest.and the amount to pay will increase by L × apr/100→ total to pay = L + L × apr/100 = L(1 + apr/100)→ Annual rate = 1 + apr/100Now assuming no payments are made for 12 periods with a periodpercentage rate of ppr%→ amount to pay = L(1 + ppr/100)×(1 + ppr/100)×...×(1 + ppr/100)= L(1 + ppr/100)¹²The rate for one of the periods is the 12th root of the rate toget the interest added after 12 periods.If the period is a month, then 12 monthly periods = 1 year→ the monthly rate is the 12th root of the annual rate→ monthly rate (r) = (1 + apr/100)^(1/12)Then:After 1 month, the amount remaining to pay is Lr - pAfter 2 months, the amount remaining to pay is (Lr - p)r - p =Lr² - p(r + 1)After 3 months, the amount remaining to pay is (Lr² - p(r + 1))r- p = Lr³ - p(r² + r + 1)After n months, the amount remaining to pay is Lrⁿ - p(rⁿ⁻¹ +rⁿ⁻² + ... + r + 1)rⁿ⁻¹ + rⁿ⁻² + ... + r + 1 is a GP with sum = (rⁿ - 1)/(r -1)→ amount to pay after n months = Lrⁿ - p(rⁿ - 1)/(r - 1)If the loan is paid off after n months, then the monthly paymentcan be calculated:0 = Lrⁿ - p(rⁿ - 1)/(r - 1)→ p(rⁿ - 1)/(r - 1) = Lrⁿ→ p = Lrⁿ(r - 1)/(rⁿ - 1)Similarly, The Loan amount can be calculated:0 = Lrⁿ - p(rⁿ - 1)/(r - 1)→ Lrⁿ = p(rⁿ - 1)/(r - 1)→ L = p(rⁿ - 1)/(rⁿ(r - 1))It is up to you to insert the relevant figures for p and r(calculated from APR).----------------------------------------------------------------If it is simple interest applied for the full period, then:r is calculated slightly differently:As the interest is only dependent upon the number ofperiods:Interest = L × apr/100 × number of yearsThe monthly rate is 1/12 the annual rate as simple interestassumes the same amount added per period and 1 year = 12 monthlyperiodsThis gives:amount to repay = L(1 + apr/100 × n/12) = pn→ L = pn/(1 + n × apr/1200)where apr = annual percentage rateL = loanp = monthly paymentn = number of months.---------------------------------------------------------------Of note is that when I financed the purchase of my car, theycalculated the monthly payment based on simple interest, ie theyadded simple interest for the period of the loan and then dividedthis by the number of months By doing this the compounded APR (the"representative APR" given to allow comparison with other loansavailable) is higher than the simple APR as the simple APR ignoresthe fact that part of the monthly payments are repaying part of theloan and so not the whole loan is borrowed for the whole period;the proportion of the monthly repayment that is the loan increasesas the time progresses towards the end of the loan period.An interest only mortgage works in a similar way to simpleinterest - your monthly payments are lower as you are only payingback the interest accrued each month. At the end of the mortgageperiod you have the find the capital to pay off the WHOLE of thevalue loaned from somewhere: this led to endowment mortgages whereyou paid interest only to the mortgage provider and also paid somemoney into a fund that you hoped would gain enough interest to haveenough in the pot to cover the whole of the mortgage loaned (withsome extra). If the fund did not perform as well as expected, youwould end up with a deficit in your pot you would need to find fromsomewhere.

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